Since deciding to homeschool my son I have done a lot of reading about the different ways we learn. It sounds like your son is a kinesthetic learning. He learns best and he is engaged when his mind and hands are busy. When he is doing projects, labs, and is engages in class discussion he is fully engaged. He can focus and his brain retains the information better.
I understand that you are in a small school district but there are still things that he, they, and you can do so that he learns. That is, after all, there job and it's the one job I think schools are sadly overlooking these days - teaching him how to learn. I think it's way more important that he learns than it is that he learns THEIR WAY. That's ridiculous and, in my opinion, discriminatory.
In class, let him sit in the back of the class, so that when he feels himself starting to lose focus he has stand up and move around in the back of the room. This doesn't have to be loud or distracting. He can do the same thing when he is doing an assignment or reading assigned material. It will help him regain his focus.
Let him take notes in class lectures and while reading book texts that allow him to be engaged. He can write them on notecards and organize them. If he has to shuffle and reorganize them, not only is it a good study tool but his brain and hands are engaged.
He can be allowed to record lectures and class discussions and listen to them again when he is at home and working with his hands or taking a walk with mom. Again, it will help him to focus.
Start at home and ask the teachers in class to work out a system where he works for ten minutes, then gets up for a minute and stretches his legs.
He shouldn't be a disruption to the class, but if you focus now on how he learns and retains information the best way, this could be a huge gift when he is older. He will feel more successful and his teachers will be less frustrated.
I strongly recommend the book Learning Outside the Lines by Jonathan Mooney and David Cole. It has been invaluable in helping me understand my son and him understanding himself and well as giving great tools for alternative learners.
Hope this helps
L.